True, but do definitions not encourage a more thorough analysis?
If A is a male, B is a female, C is a male, your operator definition is even troublesome within a species.
What kind of mathematical object comes closer to this abstraction of a species? Maybe it's not about names and boundaries, but about getting to understand things for which you need abstractions.
I always appreciate when people do not fuss about definitions and easily change them but reason consistently after indicating their interpretation of those concepts.
I don’t think your example really applies, because no one expects the definition of “species” to imply that the “individual A can mate with individual B” relation to be transitive.
Agreed, of course we need definition to discuss, and indeed we should be fluent about them. This is difficult to explain to a child or indeed to some adults.
If A is a male, B is a female, C is a male, your operator definition is even troublesome within a species.
What kind of mathematical object comes closer to this abstraction of a species? Maybe it's not about names and boundaries, but about getting to understand things for which you need abstractions.
I always appreciate when people do not fuss about definitions and easily change them but reason consistently after indicating their interpretation of those concepts.